Buckling of skew plates and corner condition for simply supported edges

Abstract

The paper considers the elastic buckling of skew plates subjected to in-plane loadings. The buckling analysis is performed using the Rayleigh-Ritz method with the newly proposed pb-2 Ritz functions, which consist of the product of a two-dimensional polynomial function and a basic function. The basic function is formed from taking the product of the equations of the boundaries, with each equation raised to the power of 0, 1, or 2 corresponding to free, simply supported, or clamped edges; thus satisfying the kinematic boundary conditions at the outset. With pb-2 Ritz functions, the analyst avoids the difficulty of searching for the appropriate function for any arbitrarily shaped plates with various combinations of supporting-edge conditions. Using this efficient and accurate pb-2 Rayleigh-Ritz method, buckling solutions are obtained and presented in the form of design charts for skew differing viewpoints on the kinematic condition for a corner formed by two simply supported edges are discussed.